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The frequency polygon shows the ages of the patients who visited a clinic in one day, using classes of width 10. The orange point stands for one class. Which class interval is it, and how many patients are in it?

Class 9StatisticsStatistics and Probability
  • A45–55; 18 patients
  • B40–50; 45 patients
  • C40–50; 18 patients
  • D35–45; 18 patients

Step-by-Step Solution

Points of a frequency polygon are plotted at class marks. The orange point is at with height ; a class of width with class mark is .
Answer: C) 40–50; 18 patients

Key idea: Class intervals and class marks

When data has many distinct values (like heights or weights), group it into **class intervals**.

Example table:
| Class interval | Frequency |
|---|---|
| 0–10 | 5 |
| 10–20 | 8 |
| 20–30 | 4 |

**Class mark** of an interval = (lower limit + upper limit) / 2.
For 0–10: mark = 5. For 10–20: mark = 15.

**Inclusive vs exclusive intervals**:
- Exclusive (continuous) form like 0–10, 10–20: 10 belongs to the SECOND interval, not the first.
- Inclusive form 0–9, 10–19: rare in modern textbooks — convert to continuous form (subtract 0.5 from lower, add 0.5 to upper) before drawing histograms.

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